| dc.contributor.author | Dostál, Zdeněk | |
| dc.date.accessioned | 2007-08-30T12:43:18Z | |
| dc.date.available | 2007-08-30T12:43:18Z | |
| dc.date.issued | 1997 | |
| dc.identifier.citation | SIAM Journal on Optimization. 1997, vol 7, issue 3, p. 871-887. | en |
| dc.identifier.issn | 1052-6234 | |
| dc.identifier.issn | 1095-7189 | |
| dc.identifier.uri | http://hdl.handle.net/10084/62377 | |
| dc.language.iso | en | en |
| dc.publisher | Society for Industrial and Applied Mathematics | en |
| dc.relation.ispartofseries | SIAM Journal on Optimization | en |
| dc.relation.uri | https://doi.org/10.1137/S1052623494266250 | en |
| dc.subject | quadratic programming | en |
| dc.subject | conjugate gradients | en |
| dc.subject | inexact subproblem solution | en |
| dc.subject | projected search | en |
| dc.title | Box constrained quadratic programming with proportioning and projections | en |
| dc.type | article | en |
| dc.identifier.location | Není ve fondu ÚK | en |
| dc.description.abstract-en | Two new closely related concepts are introduced that depend on a positive constant $\Gamma$. An iteration is proportional if the norm of violation of the Kuhn--Tucker conditions at active variables does not excessively exceed the norm of the part of the gradient that corresponds to free variables, while a progressive direction determines a descent direction that enables the released variables to move far enough from the boundary in a step called proportioning. An algorithm that uses the conjugate gradient method to explore the face of the region defined bythe current iterate until a disproportional iteration is generated is proposed. It then changes the face by means of the progressive direction. It is proved that for strictly convex problems, the proportioning is a spacer iteration so that the algorithm converges to the solution. If the solution is nondegenerate then the algorithm finds the solution in a finite number of steps. Moreover, a simple lower bound on $\Gamma$ is given to ensure finite termination even for problems with degenerate solutions. The theory covers a class of algorithms, allowing many constraints to be added or dropped at a time and accepting approximate solutions of auxiliary problems. Preliminary numerical results are promising. | en |
| dc.identifier.doi | 10.1137/S1052623494266250 | |
| dc.identifier.wos | 000071020000015 | |